No one claimed that. The point was that Valve controls the API and can cut access to said API to the gambling sites. This is not like sports betting, where the gambling sites don't need any integration with the actual sport : if Valve wants, they can seriously affect the abity of the sites to function.
I don't think they tried very hard to shut them down, they could be doing a lot more.
Edit: based on what I recall from this Coffeezilla video (https://youtu.be/13eiDhuvM6Y?si=GJ_kXOJyXFTogy40&t=476)